Simple CS assignment

CNS 3320 – Numerical Software Development
Program 1
Calculate ulps of Two Numbers

Write a function, ulps(x,y), that takes two floating point parameters, x and y, and returns
the number of ulps (floating-point intervals) between x and y. You will of course need to
take into account that x and y may have different exponents of the floating-point base in
their representation. Also, do not assume that x <= y (handle either case). Your function
may assume that its parameter will be the floating-point type. Do not use logarithms to
find the exponent of your floating-point numbers – use repeated multiplication/division
following the pattern discussed in class. Your function should handle negative numbers
and numbers less than 1.

Your function will return infinity if the input parameters have the following properties:
? Opposite in signs, or
? Either one of them is zero, or
? Either one of them is either positive infinity or negative infinity.

If the input parameters are both negative, convert them to be positive numbers by taking
the absolute value. Your algorithm only needs to work with two positive floating-point
numbers.

The following code segment shows how to use math and sys modules to get the base,
infinity (inf), machine epsilon (eps), and mantissa digits (prec) in Python.
import sys
import math
base = sys.float_info.radix
eps = sys.float_info.epsilon
prec = sys.float_info.mant_dig
inf = ---------- f

Algorithm analysis:
1. Check the input parameters for special conditions.
2. Find the exponents for both input parameters in the machine base (base).
For example: Find exp such that (????????????????)???????????? ????? <(????????????????)????????????+1.
3. Examine the exp for both parameter:
a. If they are the same: count the intervals between them. (Remember that
the spacing is ????????????? for each interval [????????,????????+1])
b. If they differ by one: add the intervals from the smaller number to ????????????????+1
to the intervals from ????????????????+1 to the larger number.
c. If they differ by more than one: In addition to the number of intervals in
part b, add the numbers of intervals in the exponent ranges in between the
exponents of these two numbers.

Verify your algorithm with the following inputs with my answers which are listed after
each call:
print(ulps(-1.0, -1. ---------- )) //1
print(ulps(1.0, 1. ---------- )) //1
print(ulps(1.0, 1. ---------- )) //2
print(ulps(1.0, 1. ---------- )) //2
print(ulps(1.0, 1. ---------- )) //3
print(ulps(0. ---------- , 1.0)) //1
print(ulps(0. ---------- , 2.0)) // ---------- print(ulps(0. ---------- , 2.0)) // ---------- print(ulps(0.5, 2.0)) // ---------- print(ulps(1.0, 2.0)) // ---------- print(2.0**52) // ---------- .0
print(ulps(-1.0, 1.0) //inf
print(ulps(-1.0, 0.0) //inf
print(ulps(0.0, 1.0) //inf
print(ulps(5.0, ---------- f) //inf
print(ulps(15.0, 100.0)) // ---------- Submission:
Submit your source code and a screenshot of your program outputs.

Python is the preferred language of this class. If you choose a different language, please
work with the course IA to ensure that your submission can be executed with his
environment and verify your results.